I disagree with the general sentiment here. This strikes me as begging the question or circular reasoning, whichever way of putting it you prefer. That is, we’re trying to prove that God exists, so using his existence as proof of his existence is pretty much a text book case of that.
That said, I think the point he’s trying to make is that existence would necessarily leave some form of evidence that would allow us to prove his existence and then that evidence would then be used to prove it. So, like using the “my thumb exists because it exists” assertion, it produces visual evidence, in that I can see it, and it can be used to interact with the environment in some measurable way. But that’s just my assumption on what he might have meant and one would still have to agree on what evidence God’s existence might or might not generate and whether or not that proves he exists.
This is probably drifting into GD territory, but this argument is common and it bugs me too, mostly because I think it’s a gross simplification of various beliefs of God. Yes, some or even many theists argue that only their very specific set of properties for God is true and anything else is just plain false, and that’s what this sort of argument would work for, but there’s other ways to look at it. For instance, there may be some dispute about it but as a general rule, the Abrahamic faiths more or less claim to believe in the same God, they just disagree about some of the specifics. I know plenty of Christians and Jews who seem sympathetic that, even though they might argue followers of non-Abrahamic faiths might go to hell or whatever, at least sects of their faith or sister faiths are not. Some various polytheistic views argue that many gods or perspectives of perhaps some larger entity exist and they just have chosen a certain one or ones for various reasons. Extending that, some believe that the creator or creators or whatever exist, we all just have various experiences and ideas about the nature of that being, and so no one is completely wrong, particularly as it is experiential, or for that matter, no one is probably completely right about the nature of God (or whatever replacement term they use). Similarly, I know plenty of people who believe this and accept various other religious views, Christian, Jewish, Hindu, Buddhist, etc. So, I don’t think one can really argue that any of those would fit the “2799/2800” atheist assertion.